Combining Inverse Probability Weighting and Multiple Imputation to Improve Robustness of Estimation

Inverse probability weighting (IPW) and multiple imputation are two widely adopted approaches dealing with missing data. The former models the selection probability, and the latter models data distribution. Consistent estimation requires correct specification of corresponding models. Although the augmented IPW method provides an extra layer of protection on consistency, it is usually not sufficient in practice as the true data‐generating process is unknown. This paper proposes a method combining the two approaches in the same spirit of calibration in sampling survey literature. Multiple models for both the selection probability and data distribution can be simultaneously accounted for, and the resulting estimator is consistent if any model is correctly specified. The proposed method is within the framework of estimating equations and is general enough to cover regression analysis with missing outcomes and/or missing covariates. Results on both theoretical and numerical investigation are provided.     

Joint GEEs for multivariate correlated data with incomplete binary outcomes

This study considers a fully-parametric but uncongenial multiple imputation (MI) inference to jointly analyze incomplete binary response variables observed in a correlated data settings. Multiple imputation model is specified as a fully-parametric model based on a multivariate extension of mixed-effects models. Dichotomized imputed datasets are then analyzed using joint GEE models where covariates are associated with the marginal mean of responses with response-specific regression coefficients and a Kronecker product is accommodated for cluster-specific correlation structure for a given response variable and correlation structure between multiple response variables. The validity of the proposed MI-based JGEE (MI-JGEE) approach is assessed through a Monte Carlo simulation study under different scenarios. The simulation results, which are evaluated in terms of bias, mean-squared error, and coverage rate, show that MI-JGEE has promising inferential properties even when the underlying multiple imputation is misspecified. Finally, Adolescent Alcohol Prevention Trial data are used for illustration.     

A Weighting Approach for GEE Analysis with Missing Data

We propose a new weighting (WT) method to handle missing categorical outcomes in longitudinal data analysis using generalized estimating equations (GEE). The proposed WT provides a valid GEE estimator when the data are missing at random (MAR), and has more stable weights and shows advantage in efficiency compared to the inverse probability weighing method in the presence of small observation probabilities. The WT estimator is similar to the stabilized weighting (SWT) estimator under mild conditions, but it is more stable and efficient than SWT when the associations of the outcome with the observation probabilities and the covariate are strong.     

Penalized inverse probability weighted estimators for weighted rank regression with missing covariates

Abstract

In this article, we study the variable selection and estimation for linear regression models with missing covariates. The proposed estimation method is almost as efficient as the popular least-squares-based estimation method for normal random errors and empirically shown to be much more efficient and robust with respect to heavy tailed errors or outliers in the responses and covariates. To achieve sparsity, a variable selection procedure based on SCAD is proposed to conduct estimation and variable selection simultaneously. The procedure is shown to possess the oracle property. To deal with the covariates missing, we consider the inverse probability weighted estimators for the linear model when the selection probability is known or unknown. It is shown that the estimator by using estimated selection probability has a smaller asymptotic variance than that with true selection probability, thus is more efficient. Therefore, the important Horvitz-Thompson property is verified for penalized rank estimator with the covariates missing in the linear model. Some numerical examples are provided to demonstrate the performance of the estimators.     

Verification bias on sensitivity and specificity measurements in diagnostic medicine: a comparison of some approaches used for correction

Verification bias may occur when the test results of not all subjects are verified by using a gold standard. The correction for this bias can be made using different approaches depending on whether missing gold standard test results are random or not. Some of these approaches with binary test and gold standard results include the correction method by Begg and Greenes, lower and upper limits for diagnostic measurements by Zhou, logistic regression method, multiple imputation method, and neural networks. In this study, all these approaches are compared by employing a real and simulated data under different conditions.     

Inference and Missing Data: Asymptotic Results

In Rubin (1976) the missing at random (MAR) and missing completely at random (MCAR) conditions are discussed. It is concluded that the MAR condition allows one to ignore the missing data mechanism when doing likelihood or Bayesian inference but also that the stronger MCAR condition is in some sense the weakest generally sufficient condition allowing (conditional) frequentist inference while ignoring the missing data mechanism. In this paper it is shown that (a slightly strengthened version of) the MAR condition is sufficient to yield ordinary large sample results for estimators and test statistics and thus may be used for (asymptotic) frequentist inference.     

Different methods for handling incomplete longitudinal binary outcome due to missing at random dropout

This paper compares the performance of weighted generalized estimating equations (WGEEs), multiple imputation based on generalized estimating equations (MI-GEEs) and generalized linear mixed models (GLMMs) for analyzing incomplete longitudinal binary data when the underlying study is subject to dropout. The paper aims to explore the performance of the above methods in terms of handling dropouts that are missing at random (MAR). The methods are compared on simulated data. The longitudinal binary data are generated from a logistic regression model, under different sample sizes. The incomplete data are created for three different dropout rates. The methods are evaluated in terms of bias, precision and mean square error in case where data are subject to MAR dropout. In conclusion, across the simulations performed, the MI-GEE method performed better in both small and large sample sizes. Evidently, this should not be seen as formal and definitive proof, but adds to the body of knowledge about the methods’ relative performance. In addition, the methods are compared using data from a randomized clinical trial.     

Adaptive nonparametric density estimation with missing observations

It is well known that if some observations in a sample from the probability density are not available, then in general the density cannot be estimated. A possible remedy is to use an auxiliary variable that explains the missing mechanism. For this setting a data-driven estimator is proposed that mimics performance of an oracle that knows all observations from the sample. It is also proved that the estimator adapts to unknown smoothness of the density and its mean integrated squared error converges with a minimax rate. A numerical study, together with the analysis of a real data, shows that the estimator is feasible for small samples.     

Handling the effect of non-response in graphical models for longitudinal data

In this paper we investigated the use of attrition weights to cope with non-response when selecting graphical chain models for longitudinal data. We proposed a parametric bootstrap approach to account for the extra variability introduced by the estimation of the weights and compared this with results using standard test procedures.     

Working With Missing Values

Less than optimum strategies for missing values can produce biased estimates, distorted statistical power, and invalid conclusions. After reviewing traditional approaches (listwise, pairwise, and mean substitution), selected alternatives are covered including single imputation, multiple imputation, and full information maximum likelihood estimation. The effects of missing values are illustrated for a linear model, and a series of recommendations is provided. When missing values cannot be avoided, multiple imputation and full information methods offer substantial improvements over traditional approaches. Selected results using SPSS, NORM, Stata (mvis/micombine), and Mplus are included as is a table of available software and an appendix with examples of programs for Stata and Mplus.